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					Cosmology

  Dr Bryce
   29:50
         Basic Observations
 At the beginning of the semester our basic
  observations were that sky gets dark at
  night, the Sun rises in the East sets in the
  West, days are shorter in Winter/longer in
  summer
 From these observations we developed
  our model, the Earth is rotating, the
  Earth’s rotation axis is tilted
            Basic Observations
   When considering the Universe as a whole, what
    are our basic observation?
   Stars exist in galaxies and galaxies exist in
    clusters and clusters exist in super clusters
   Galaxies are receding from each other
   The further we look away from the Milky Way the
    younger the galaxies we see (blue light/low
    metalicity) and the oldest galaxies are closest to
    us
   The oldest stars we see are about 12 billion
    years old
           The standard model
     When we put these observations together we
             come up with the standard model
   The Universe is expanding
   The Universe had a “starting” point (i.e. the
    Universe has a finite age)
   The laws of physics are the same everywhere in
    the Universe
   The Universe is all made of the same matter
    (stars, gas, dust, photons etc)
   We are not located at a special point in the
    Universe
Olbers’ Paradox

If universe were

1) infinite

2) unchanging

3) everywhere
   the same

Then, stars
would cover the
night sky
Night sky is dark
because the
universe
changes with
time

As we look out
in space, we
can look back to
a time when
there were no
stars
      Cosmological Principle
     On large scales the Universe is both
          homogeneous and isotropic
                     OR
    The Universe is the same everywhere
Homogeneous: same qualities
Isotropic: independent of direction
         Copernican Principle
   Named for Nicholas Copernicus (Sun
    centre-ed solar system)

The Earth is not at a central or in anyway
              special position
     Quantifying the Universe
 How many galaxies are in the Universe?
 What is the typical mass of a Galaxy?
 Do all galaxies have significant dark
  matter components?
We measure the mass of the solar system using the
orbits of planets
• Orb. Period
• Avg. Distance


Or for circles:
• Orb. Velocity
• Orbital Radius
                       Rotation
   Possible models for rotation
   Wheel or Merry-go-round
   Planetary or Keplerian
   Milky Way doesn’t rotate like either of these models
The visible
portion of a
galaxy lies
deep in the
heart of a
large halo
of dark
matter
We can
measure
rotation
curves of
other spiral
galaxies
using the
Doppler
shift of the
21-cm line
of atomic H
Spiral galaxies all tend to have flat rotation curves
indicating large amounts of dark matter
Broadening of
spectral lines in
elliptical galaxies
tells us how fast
the stars are
orbiting

These galaxies
also have dark
matter
We can
measure
the
velocities of
galaxies in
a cluster
from their
Doppler
shifts
The mass
we find
from
galaxy
motions in
a cluster is
about
50 times
larger than
the mass
in stars!
Clusters contain
large amounts of
X-ray emitting hot
gas

Temperature of hot
gas (particle
motions) tells us
cluster mass:

 85% dark matter
 13% hot gas
  2% stars
Gravitational lensing, the bending of light rays by
gravity, can also tell us a cluster’s mass
All three methods of measuring cluster mass
indicate similar amounts of dark matter
                  Our Options

1.   Dark matter really exists, and we are
     observing the effects of its gravitational
     attraction

2.   Something is wrong with our understanding
     of gravity, causing us to mistakenly infer the
     existence of dark matter
                  Our Options

1.   Dark matter really exists, and we are
     observing the effects of its gravitational
     attraction

2.   Something is wrong with our understanding
     of gravity, causing us to mistakenly infer the
     existence of dark matter

Because gravity is so well tested, most
   astronomers prefer option #1
              Types of Dark Matter

   Ordinary Dark Matter (MACHOS)
     Massive Compact Halo Objects:
       dead or failed stars in halos of galaxies

   Extraordinary Dark Matter (WIMPS)
     Weakly Interacting Massive Particles:
       mysterious neutrino-like particles
MACHOs
occasionally make
other stars appear
brighter through
lensing

… but not enough
lensing events to
explain all the
dark matter
                      WIMPs

   There’s not enough ordinary matter, WIMPS are
    not ordinary matter

   WIMPs could be left over from Big Bang

   Models involving WIMPs explain how galaxy
    formation works
            Superclusters
 Superclusters are clusters of clusters
 Our address becomes Solar System, Milky
  Way, Local Group, Local Supercluster
 Region of space about 40 Mega Parsec
  across and is centred on the Virgo cluster
 The space between the clusters is empty
The Virgo Supercluster
        Structure beyond the local
               Supercluster
   Remember the
    distribution is three
    dimensional
   The superclusters
    often form “sheets”
   And there are
    significant voids
Galactic surveys
           Observe a “slice” of
            the Universe
           Show that galaxies
            occupy strands and
            sheets
           The voids may
            contain dark matter
            as we are only
            mapping the light
Galactic Surveys
Maps of galaxy positions reveal extremely large
structures: superclusters and voids
Dark matter is
still pulling
things together

After correcting
for Hubble’s
Law, we can
see that
galaxies are
flowing toward
the densest
regions of space
                 Time in billions of years

0.5        2.2            5.9            8.6        13.7




13         35              70            93          140

       Size of expanding box in millions of light-years
Models show that gravity of dark matter pulls
mass into denser regions – universe grows
lumpier with time
Structures in galaxy maps look very similar to the
ones found in models in which dark matter is WIMPs
            Contents of Universe


   “Normal” Matter:        ~ 4.4%
       Normal Matter inside stars: ~ 0.6%
       Normal Matter outside stars:      ~ 3.8%
   Dark Matter:            ~ 25%
   Dark Energy             ~ 70%
               Unseen Influences

Dark Matter: An undetected form of mass that emits little
  or no light but whose existence we infer from its
  gravitational influence

Dark Energy: An unknown form of energy that seems to
  be the source of a repulsive force causing the expansion
  of the universe to accelerate
         The expansion age
 Expansion implies that there was a time at
  which everything was close together
 From the exapansion rate we can
  calculate the amount of time the Universe
  has been expanding
 If you have driven 180 miles at 60 mph,
  how long have you been driving for
                      1
                   t
                      H
   Assumes that the expansion rate of the Universe
    doesn’t change
   Called the Hubble time
   Large values of H give us a young Hubble time
    and small values give us old Hubble time
   For example if early expansion happened at a
    slower rate than we observe currently the age of
    the Universe will be older than the Hubble time
          General relativity
 General relativity describes the behaviour
  of spacetime in the presence of matter
 General relativity gives us the
  mathematical tools required to study the
  Universe “Field Equations”
 Allows us to develop cosmological models
  in which we consider the properties of
  space
 Is spacetime curved or flat?
Positive Curvature
          Positive Curvature
 Living on the surface of the Earth it is hard
  to detect that the Earth is curved
 The surface of the Earth is finite
 Likewise if the Universe has positive
  curvature it would be finite in extent
 There are no boundaries
 There is no centre to the surface, no
  unique points on the surface of a sphere
Flat space
               Flat Space
 The easiest option for us to visualize
 Familiar geometric properties
 2-dimensional flat space has infinite area
  and could contain infinite mass
 There are no boundaries
 There is no centre
Negative curvature
         Negative Curvature
 Saddle shaped
 Has infinite area and can have infinite
  mass
 As with flat and positively curved space
  there are no boundaries
 There is no centre
          Testing Curvature
 Which type of Universe do we live in?
 What type of geometry matches our
  observations?
 What is the circumference of a large circle,
  the sum of angles in a large triangle?
            Galaxy counts
 Instead of “drawing” large circles or
  triangles we can count the number of
  galaxies within circles of different radii
 This assumes that the density of galaxies
  is uniform on large scales
 For flat space the number will increase
  according to pr2, for negatively curved
  space it will increase more quickly and
  positively curved space more slowly
           Complications
 Galaxies are expanding, the density is
  changing with time
 Galaxies change with time causing their
  luminosities to change, making them more
  difficult to see
                 Density
 General relativity tells us the matter (and
  consequently energy) determines the
  curvature of spacetime
 So the density of the Universe is related to
  the curvature of the Universe
 A large value of density will give us a
  positively curved Universe
 A small value of density will give us a
  negatively curved Universe
            Critical density
 The density of a flat Universe, i.e. the
  division between positive and negative
  curvature
 A slightly denser Universe would be
  positively curved and slightly less dense
  would be negatively curved
 Critical density rc=10-26kg/m3
 About 10 hydrogen atoms per cubic meter
       Critical density parameter
   Estimates of the density
    of energy and matter in


                                    r
    the Universe are always
    compared to the critical

                               o 
    density
   Astronomers use this


    ratio
    If less than 1 negative
    curvature
                                    rc
   If more than 1 positive
    curvature
    What makes up the density
 All normal matter, us, stars, gas, dust
 All photons
 All neutrinos
 Dark matter
 Forms of energy that we do not yet know
  of
       The role of expansion
 If the Universe is made up of the matter
  and energy we can see and infer, then
  expansion is slowing down because of the
  gravitational pull of the Universe itself.
 Consider throwing a ball up and down…
 The escape velocity is the velocity with
  which the ball can escape from Earth’s
  gravitational field
Does the universe have enough kinetic
 energy to escape its own gravitational
 pull?
 This depends on the rate of expansion
  (the Hubble constant) and the average
  density of the Universe
 A slow expansion and high density will
  result in a Universe that will reach a
  maximum size stop expanding and start
  contracting
 A fast expansion and low density will result
  in a Universe that will expand forever
Expansion scenarios
                                         Fate of
                                         universe
                                         depends
                                         on the
                                         amount
                                         of dark
                                         matter




              Critical
Lots of                    Not enough
              density of
dark matter                dark matter
              matter
Amount of dark
matter is ~25% of
the critical density
suggesting fate is
eternal expansion

                       Not enough
                       dark matter
But expansion
appears to be
speeding up!




  Dark          Not enough
  Energy?       dark matter
             Dark Energy
 Energy associated with the acceleration of
  the expansion rate
 Einstein included a “cosmological
  constant” in his famous field equations to
  allow a static solution.
 Matter slows expansion whereas dark
  energy accelerates expansion
                     Fig.26.12




As the density of the Universe decreases the dominant
  force changes from matter to dark energy
        old
                 older
                               oldest
Estimated age depends on both dark matter and
dark energy
Brightness of distant white-dwarf supernovae tells us
how much universe has expanded since they exploded
Accelerating universe is best fit to supernova data
                 Results
 Distant supernova are brighter than their
  redshift suggests, i.e. expansion was
  slower in the past
 Universe is very close to being flat with
  27% of the density supplied by normal
  mass and energy and 73% supplied by
  dark energy
 The Hubble constant is 70km/s per Mpc
 The age of the Universe is 13.7 billion year
The early
universe
must have
been
extremely
hot and
dense
 Photons converted into particle-antiparticle
  pairs and vice-versa
 E = mc2
 Early universe was full of particles and
  radiation because of its high temperature
Planck Era

Before
Planck time
(~10-43 sec)

No theory of
quantum
gravity
GUT Era

Lasts from
Planck time
(~10-43 sec)
to end of
GUT force
(~10-38 sec)
Electroweak
Era

Lasts from
end of GUT
force (~10-38
sec) to end of
electroweak
force (~10-10
sec)
Four known forces
in universe:
 Strong Force
 Electromagnetism
 Weak Force
 Gravity
Particle Era

Amounts of
matter and
antimatter
nearly equal

(Roughly 1
extra proton
for every 109
proton-
antiproton
pairs!)
Era of
Nucleo-
synthesis

Begins when
matter
annihilates
remaining
antimatter at
~ 0.001 sec

Nuclei begin
to fuse
Era of Nuclei

Helium nuclei
form at age
~ 3 minutes

Universe has
become too
cool to blast
helium apart
Era of Atoms

Atoms form
at age ~
380,000
years

Background
radiation
released
Era of
Galaxies

Galaxies form
at age ~ 1
billion years
         Primary Evidence

1) We have detected the leftover
   radiation from the Big Bang.

2) The Big Bang theory correctly predicts
   the abundance of helium and other
   light elements.
The cosmic
microwave
background –
the radiation
left over from
the Big Bang –
was detected
by Penzias &
Wilson in
1965
Background radiation from Big Bang has been
freely streaming across universe since atoms
formed at temperature ~ 3,000 K: visible/IR
Before and After recombination
Small fluctuations in the CMB
                     Background has perfect
                     thermal radiation
                     spectrum at temperature
                     2.73 K




Expansion of universe has redshifted thermal
radiation from that time to ~1000 times longer
wavelength: microwaves
Cosmic Microwave Background
 Close to perfect blackbody spectrum
 Temperature of 2.725K
 Same temperature in every direction
 Temperature variations are very very small
  ~0.0001K
 CMB is the surface of last scattering
 Oldest object we can observe
Protons and neutrons combined to make long-
lasting helium nuclei when universe was ~ 3
minutes old
Big Bang theory prediction: 75% H, 25% He (by
mass)

Matches observations of nearly primordial gases
Inflation addresses three issues

1) Where does structure come from?

2) Why is the overall distribution of matter
   so uniform?

3) Why is the density of the universe so
   close to the critical density?
Inflation can
make all the
structure by
stretching tiny
quantum ripples
to enormous
size

These ripples in
density then
become the
seeds for all
structures
How can microwave temperature be nearly
identical on opposite sides of the sky?
Regions now
on opposite
sides of the
sky were
close together
before
inflation
pushed them
far apart
                      Overall
                      geometry of
Density = Critical    the universe is
                      closely related
                      to total density
                      of matter &
                      energy
Density > Critical




 Density < Critical
Inflation of
universe
flattens overall
geometry like
the inflation of
a balloon,
causing overall
density of
matter plus
energy to be
very close to
critical density
Inflation
Patterns of structure observed by WMAP show us
the “seeds” of universe
Observed patterns of structure in universe agree (so
far) with the “seeds” that inflation would produce
   “Seeds” Inferred from CMB

• Overall geometry is flat
  – Total mass+energy has critical density
• Ordinary matter ~ 4.4% of total
• Total matter is ~ 27% of total
  – Dark matter is ~ 23% of total
  – Dark energy is ~ 73% of total
• Age of 13.7 billion years
              Dark Matter
 Matter that doesn’t reflect or emit light
 Inferred from gravitational interactions
 Is important for structure formation
 Contemporary evidence suggests that
  dark matter is most likely new elementary
  particles (often called non baryonic dark
  matter)
              Dark Energy
 Hypothetical form of energy that produces
  an acceleration in the rate of expansion of
  the Universe
 Presence of Dark Energy is also indicated
  by measurements of the cosmic
  microwave background, gravitational
  lenses and the large scale structure of the
  Universe
          Non standard Models
   Steady State Universe; the Universe is
    infinite in extent and relatively unchanging.
    It cannot explain the presence of the
    cosmic microwave background
         Non standard models
   Tired light; instead of the observed
    redshifts being due to expansion they are
    due to the photons losing energy on the
    journey to us. Incorrect as the light we see
    isn’t blurred and the physical processes by
    which the photons would lose energy
    would cause blurring
           Philosophical points
   Omphalos; the idea that the Universe was
    made to look old in order to be functional,
    completely unverifiable and unfalsifiable.
    NOT a scientific theory
                 Fine tuning

    Small changes in physical constants such
    as G would have a huge impact on the
    Universe, for example whether or not stars
    could shine. The conditions that allow life
    depend on these constants being correct.
    Counterargument is that many failed
    Universes could have existed. Again not
    testable.
         Anthropic Principle
 We must remember that we can only
  observe our Universe because we are in it!
 The existence of multiple universes or a
  designer are highly controversial and as
  these ideas are un-testable this means
  that they outside the realms of science, no
  matter how interesting they may be
  philosophically.

				
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posted:3/31/2011
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